Affine Lie algebras and quantum groups

TLDR: In this paper, a tensor structure on a category of representations of affine Lie algebras is defined, and the tensor category of finite-dimensional representations of a quantized enveloping algebra is identified.

Abstract: Let g be a finite dimensional simple Lie algebra of simply laced type. Drinfeld has shown that the tensor category of finite-dimensional representations of the corresponding quantized enveloping algebra over formal power series is equivalent to a tensor category whose objects are the finite-dimensional representations of g and whose tensor structure is obtained from the Knizhnik-Zamolodchikov equations. Our paper can be considered as an extension of Drinfeld's work. Following ideas from conformal field theory we define a tensor structure on a category of representations of an affine Lie algebra, and we identify it with the tensor category of finite-dimensional representations of a quantized enveloping algebra